Question

In cyclic quadrilateral ABCD A= angle (6x + 10)^° , B = angle (5x)^°,C= angle (X + y)^°and D=angle (3y-10)^°. Find X, y and all angles

Answer 1

Answer:

130°,100°,50°,80°

Step-by-step explanation:

according to the problem,

6x+10+x+y=180

7x+y=170

y=170-7x

and also

5x+3y-10=180

5x+3(170-7x)=190

5x+510-21x=190

-16x=-320

x=20

y=170-7x

y=170-7(20)

y=170-140

y=30

A=6x+10=6(20)+10=120+10=130°

B=5x=5(20)=100°

C=x+y=20+30=50°

D=3y-10=3(30)-10=90-10=80°

Answer 2

Answer:

Here , ABCD is a cyclic quadrilateral .

so, ang.A + ang.C = 180°

=> 7x + y =170 ...... (1)

similarly, ang.B+ ang.D=180°

=> 5x+3y= 190 ....... (2)

Now, solving (1) &(2) we get:-

16x =320

=> x =20°

& y = 30°

ang.A = 130° , ang.B=100° , ang.C=50° and ang.D=80°

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